Putting it All Together: The Ptolemaic System
Claudius Ptolemy (c. 90 - c. 168 CE)
• Librarian at Alexandria
• “The Great Treatise” & “The Almagest” (to the 12th Century)
The Ptolemaic System: Objectives
Wanted : A Model to explain the observed apparent motions of the
Sun, Moon, Planets, and the Celestial Sphere.
The Model should explain related phenomena such as the lunar phases, eclipses, and planetary brightness variation.
The Model should be capable of accurately predicting these phenomena. (When? Where? Details?)
The Model is geostatic, geocentric, and uses only uniform circular motions.
( cf., the Aristotelian doctrines and the Aristarchian heresy.)

The Ptolemaic System
Observations
• The apparent rotation of the Celestial Sphere
• The annual motion of the Sun along the ecliptic
• The monthly motion of the Moon
The lunar phases and the synodic month
Lunar and Solar Eclipses
• The motions of the planets on the celestial sphere
Direct and retrograde motions
Planetary brightness variations
Periodicities: The synodic periods
Assumptions
• A Geostatic cosmology (The Earth does not move.)
• Uniform Circular motions (It is a “perfect” universe.)
Approaches
• The offsets and epicycles introduced by Hipparchus

For Inferior Planets (Mercury Venus)
Deferent Period is 1 Year; Epicyclic period is the Synodic Period
For Superior Planets (Mars, Jupiter, Saturn)
Deferent Period is the Synodic period; Epicyclic Period is 1 year

The Ptolemaic System (“To Scale”)
Note: Indicated motions are with respect to the Celestial Sphere

AGAIN:

Recollect the assumptions
• The Earth doesn ’ t move ( “geostatic” )
• The Earth is at the center of the universe ( “geocentric” )
• All motions are circular (... or combinations thereof)
• All motions are uniform (... i.e., of constant speed)
The Problems
• Complexity: Three different kinds of planets
• Complexity: Deferents, Epicycles, Equants, Tilts,..)
• Difficulty in giving accurate long-term predictions
(....resolved by increasing complexity?)
• The problem of Brightness Variations
(Are the planets spheres shining by reflected Sunlight?)
....but the Ptolemaic System was the only game in town!

• Superior Planets ( Mars, Jupiter, Saturn ) should be brightest at conjunction, faintest at opposition
- but the opposite is observed!
• Inferior Planets ( Mercury, Venus ) should be brightest at maximum elongation (broadest crescent) and fade toward superior conjunction (“new”)
- but they actually brighten!
But does this falsify the Ptolemaic System?

(Roughly 400 CE to 1000 CE)
The Classical Universe: The Ptolemaic System
Geostatic & Geocentric
Limited Predictive & Explanatory Power
The Alexandrian Library (330 BCE - 415 CE )
Bishop Theophilus (and 392 CE)
Saint Cyril (Bishop of Alexandria) and Hypathia (37 0- 415 CE)
“Evolution” of the Ptolemaic Model
Astronomy in the Arabic World
The Lengthening Time Basis
Increasing Complexity
The Renaissance
(~1300 to ~1500)
The Late Middle Ages to the Reformation

(“The Earth Moves”)
Nicolas Copernicus (1473-1543)
De Revolutionibus Orbium Coelestium (1543)
[“On the Revolutions of the Celestial Spheres”]
Various Theological and Political Issues
• Aristotle and the “Aristarcian Heresy”
• Conflicts with Aristotelian Physics and Philosophy
• Aristotle and Church Doctrine: Thomas Aquinas (1224-1274)
• Contemporary Theology: Martin Luther (1483-1546)
“Joshua commanded the Sun to stand still, not the earth.”